ON SOME EXTREMAL PROBLEMS OF THE BEST APPROXIMATION BY ENTIRE FUNCTIONS
In this paper a number of extremal problems of approximation theory of square summable functions on the whole line R : = (–∞,+∞) by entire functions of exponential type. In the space L2(R) of the exact constants of Jackson-Stechkin type inequalities were calculated. Found There was found the upper bounds approximation of classes of functions L2(R), defined with the help of the average modulus of continuity of m-th order, where instead of the shift operator ( , ): ( ) h T f x = f x + h is used Steklov’s operator Sh ( f ). Similar smoothness characteristics for solving the extremal problems of approximation theory for periodic functions in L2[0,2π] were previously considered in the works by V. A. Abilov, F. I. Abilova, S. B. Vakarchuk, M. Sh. Shabozov and others. It is proved that the obtained results in this paper are ultimate does not approving.
Keywords: the best approximation, modulus of continuity of m-order, Jakson-Stechkin type inequality, entire function of exponential type, operator of Steklova
References:
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Issue: 2, 2015
Series of issue: Issue 2
Rubric: INTERDISCIPLINARY STUDIES
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